This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to automatically establish the mathematical properties of expressions provided by ...
More

This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to automatically establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded. This is not so simple. Even articulating precisely the desired criteria forces the teacher to think very carefully indeed. Hence, CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. For example, the constraints of the paper-based formats have affected what we do and why. It is natural for busy teachers to set only those questions which can be marked by hand in a straightforward way. However, there are other kinds of questions, e.g., those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. And yet such questions have their place and value in provoking thought and learning. Furthermore, we explain how, in certain cases, these can be automatically assessed. Case studies of existing systems will illustrate this in a concrete and practical way.Less

Computer Aided Assessment of Mathematics

Chris Sangwin

Published in print: 2013-05-02

This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to automatically establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded. This is not so simple. Even articulating precisely the desired criteria forces the teacher to think very carefully indeed. Hence, CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. For example, the constraints of the paper-based formats have affected what we do and why. It is natural for busy teachers to set only those questions which can be marked by hand in a straightforward way. However, there are other kinds of questions, e.g., those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. And yet such questions have their place and value in provoking thought and learning. Furthermore, we explain how, in certain cases, these can be automatically assessed. Case studies of existing systems will illustrate this in a concrete and practical way.

Curricular Resources and Classroom Use examines the use of curricular resources, that is, the different kinds of materials (digital or physical) that teachers use in or for their teaching (textbooks, ...
More

Curricular Resources and Classroom Use examines the use of curricular resources, that is, the different kinds of materials (digital or physical) that teachers use in or for their teaching (textbooks, lesson plans, etc.). These resources have a significant influence on students’ opportunities to learn. At the same time, teachers play a crucial role as interpreters and users of curricular resources, so there is a complex relationship between curricular resources and their classroom use. Research thus far has mostly focused on developing approaches for studying either particular curricular resources or their classroom use. This book aims to bridge these highly related programs of research by describing, comparing, and exemplifying new research approaches for studying curricular resources and their classroom use, as well as the complex interplay between the two. This book exemplifies the approaches in the area of mathematics, but the approaches can be more broadly applicable and be used in isomorphic ways in other subject areas (science, history, etc.). As issues concerning curricular resources and the classroom use of such resources are of interest to researchers, curriculum developers (such as textbook authors), and teacher educators in many countries, this book is addressed to a broad international audience. In addition to providing implications for research, this book has implications for curriculum development and teacher education. Specifically, this book deepens understanding of how curriculum developers can better exploit the potential of curricular resources to support classroom work, and how teacher educators can better support teachers to use curricular resources in the classroom.Less

Curricular Resources and Classroom Use : The Case of Mathematics

Gabriel J. Stylianides

Published in print: 2016-05-01

Curricular Resources and Classroom Use examines the use of curricular resources, that is, the different kinds of materials (digital or physical) that teachers use in or for their teaching (textbooks, lesson plans, etc.). These resources have a significant influence on students’ opportunities to learn. At the same time, teachers play a crucial role as interpreters and users of curricular resources, so there is a complex relationship between curricular resources and their classroom use. Research thus far has mostly focused on developing approaches for studying either particular curricular resources or their classroom use. This book aims to bridge these highly related programs of research by describing, comparing, and exemplifying new research approaches for studying curricular resources and their classroom use, as well as the complex interplay between the two. This book exemplifies the approaches in the area of mathematics, but the approaches can be more broadly applicable and be used in isomorphic ways in other subject areas (science, history, etc.). As issues concerning curricular resources and the classroom use of such resources are of interest to researchers, curriculum developers (such as textbook authors), and teacher educators in many countries, this book is addressed to a broad international audience. In addition to providing implications for research, this book has implications for curriculum development and teacher education. Specifically, this book deepens understanding of how curriculum developers can better exploit the potential of curricular resources to support classroom work, and how teacher educators can better support teachers to use curricular resources in the classroom.

Seventy-five years of the study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals,0020and projective geometries. Matroids are of fundamental ...
More

Seventy-five years of the study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals,0020and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and structural engineering. This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. It contains over 700 exercises, and includes proofs of all of the major theorems in the subject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.Less

Matroid Theory

James Oxley

Published in print: 2011-02-17

Seventy-five years of the study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals,0020and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and structural engineering. This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. It contains over 700 exercises, and includes proofs of all of the major theorems in the subject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.

Proving in the Elementary Mathematics Classroom addresses a fundamental problem in children’s learning that has received relatively little research attention: Although proving and related concepts ...
More

Proving in the Elementary Mathematics Classroom addresses a fundamental problem in children’s learning that has received relatively little research attention: Although proving and related concepts (e.g., proof, argumentation, conjecturing) are core to mathematics as a sense-making activity, they currently have a marginal place in elementary classrooms internationally. This book takes a step toward addressing this problem by examining how the place of proving in elementary students’ mathematical work can be elevated through the purposeful design and implementation of mathematics tasks, specifically proving tasks. In particular, the book draws on relevant research and theory and classroom episodes with 8–9-year-olds from England and the United States to examine different kinds of proving tasks and the proving activity they can help generate in the elementary classroom. It examines further the role of elementary teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that can arise for them as they implement each kind of proving task in the classroom. In addition to its research contribution in the intersection of the scholarly areas of teaching/learning proving and task design/implementation, the book has important implications for teaching, curricular resources, and teacher education. For example, the book identifies different kinds of proving tasks whose balanced representation in the mathematics classroom and in curricular resources can support a rounded set of learning experiences for elementary students related to proving. It identifies further important mathematical ideas and pedagogical practices related to proving that can be studied in teacher education.Less

Proving in the Elementary Mathematics Classroom

Andreas J. Stylianides

Published in print: 2016-07-21

Proving in the Elementary Mathematics Classroom addresses a fundamental problem in children’s learning that has received relatively little research attention: Although proving and related concepts (e.g., proof, argumentation, conjecturing) are core to mathematics as a sense-making activity, they currently have a marginal place in elementary classrooms internationally. This book takes a step toward addressing this problem by examining how the place of proving in elementary students’ mathematical work can be elevated through the purposeful design and implementation of mathematics tasks, specifically proving tasks. In particular, the book draws on relevant research and theory and classroom episodes with 8–9-year-olds from England and the United States to examine different kinds of proving tasks and the proving activity they can help generate in the elementary classroom. It examines further the role of elementary teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that can arise for them as they implement each kind of proving task in the classroom. In addition to its research contribution in the intersection of the scholarly areas of teaching/learning proving and task design/implementation, the book has important implications for teaching, curricular resources, and teacher education. For example, the book identifies different kinds of proving tasks whose balanced representation in the mathematics classroom and in curricular resources can support a rounded set of learning experiences for elementary students related to proving. It identifies further important mathematical ideas and pedagogical practices related to proving that can be studied in teacher education.

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see http://www.oxfordscholarship.com/page/privacy-policy).date: 18 August 2017